An al Qaeda bomber stashing explosives in his underwear cakewalked onto a US-bound airliner after averting scans on two continents — but the federal Homeland Security chief incredibly claimed yesterday that “everything happened that should have.”

“This was one individual literally of thousands that fly and thousands of flights every year,” said Homeland Security Secretary Janet Napolitano, who called flying “very, very safe.”

“And he was stopped before any damage could be done . . . Once this incident occurred, everything happened that should have.”

Napolitano’s all-is-well assessment ran counter to that of her boss, President Obama, who called for a total review of procedures at US airports.

White House Press Secretary Robert Gibbs told NBC’s “Meet the Press” that Obama had ordered a full appraisal of anti-terror flight regulations, “to ensure that there is no clog in the bureaucratic plumbing of information.”

Napolitano’s astonishing claim in the aftermath of Umar Farouk Abdulmutallab’s failed bombing over Detroit led Rep. Peter King (R-LI) to respond, “The fact is, the system did not work.”

The latest system failure came last night at La Guardia. The Post learned that the feds questioned a Florida man after ground crew found what authorities called a “pyrotechnic” aboard a US Airways flight from Baltimore. The 4-inch-long, three-quarter-inch-wide explosive was found wedged between two seats. Authorities collared Thomas Ouelette, 67, of Bonita Springs, Fla., before he boarded his connecting Delta flight to Fort Myers, Fla. The feds said is did not appear terrorism was involved, but Ouelette did have two outstanding Florida warrants for “unlawful flight.”

Meanwhile:

* Abdulmutallab is singing to feds, telling investigators he trained for a month recently in an al Qaeda stronghold just north of the Yemeni capital of San’a, a source told The Post.

* Abdulmutallab also told the FBI he met with “the imam.” Feds believe he’s talking about the spiritual adviser who counseled the US Army shrink who killed 13 at Fort Hood in November.

* A Nigerian businessman, yesterday on the same Amsterdam-to-Detroit Northwest Airlines flight Abdulmutallab took on Christmas, locked himself in the bathroom for an hour, raising concerns about whether another attack was imminent. It turned out he was just ill.

* Abdulmutallab was moved from a hospital to a federal pen.

* It was learned that Abdulmutallab was subjected to secondary screening at Amsterdam’s Schiphol Airport beyond the normal magnetometers. It wasn’t clear if the powerful explosive substances he carried aboard could even have been detected by current screening procedures, King said.

But The Washington Post reported that such technology exists and has been deployed only on a limited basis because of concerns about privacy, cost and delays.

* Mlive.com quoted a lawyer who had been aboard the flight saying someone in Amsterdam had tried to help Abdulmutallab board without a passport.

Kurt Haskell told the Michigan news Web site that he saw the would-be terrorist walk up to the departure gate with a well-dressed man, who told the gate agent, “He [Abdulmuttallab] is from Sudan and we do this all the time.”

The man was apparently trying to generate sympathy — and explained Abdulmutallab’s lack of documents — by giving the impression he was a Sudanese refugee. Haskell said the two were referred to a manager — and he later saw Abdulmutallab on the plane.

* Abdulmutallab texted his family about three months ago telling them that he was traveling from Dubai to Yemen “for . . . Islam,” CNN reported.

Soon afterward, his father told the US Embassy in Nigeria he feared his son was set on “some kind of jihad.” But US intelligence officials deemed the information insufficient to pursue, The Washington Post reported. His name was added to the half-million entries in computer databases and basically forgotten, the paper said.

And Napolitano said the government did not have enough information to put Abdulmutallab on the “no-fly” list.

* A video emerged from a Yemeni al Qaeda operative threatening the United States. “We’re carrying a bomb to hit the enemies of God,” the terrorist said on the tape, which hit the Internet on Dec. 21.

Trying to prove that procedures worked properly, Napolitano noted that within 90 minutes of Abdulmutallab’s botched bombing, all 128 flights in the air from Europe had been notified to take additional security measures.

“Everybody played an important role here. The passengers and crew of the flight took appropriate action,” she said.

Harmful globetrotter

1. 2008: Umar Farouk Abdulmutallab first travels to the US after being granted a multi-entry visa on June 16; one of the trips reportedly was to Houston.

2. May 2009: Refused a visa to enter Britain after applyingto a bogus college, The Sunday Times of London reports.

3. October: Sends text to family that he was going to Yemen from Dubai “for the course of Islam.”

4. Dec. 16: In Ghana, pays cash for a round-trip ticket from Nigeria to Amsterdam and then Detroit.